General Expressions of Internal Displacement and Stress Fields due to a Moment Tensor in an Elastic-Viscoelastic Layered Half-Space

We succeeded in deriving general expressions of internal deformation fields due to a moment tensor in a gravitational two-layered elastic-viscoelastic half-space. In general, any indigenous source can be expressed in a form of moment tensor, and a moment tensor can be uniquely decomposed into three different types of sources corresponding to isotropic explosion, crack opening, and shear faulting. Among these three different types of sources, the expressions for shear faulting have been already obtained, but not for isotropic explosion and crack opening. To derive the expressions, we begin with the classical expressions of static displacement fields due to a moment tensor in an infinite elastic medium in Cartesian coordinates. Applying Hankel transformation to the expressions in Cartesian coordinates, we obtained the expressions in cylindrical coordinates. These expressions correspond to the special solution originated from a force term of the equilibrium equation of an infinite elastic medium. In order to obtain the general solution, the homogeneous solution for a two layered half-space must be added to the special solution. With a generalized propagator matrix method, we obtain the general expressions of internal deformation fields due to a moment tensor in a two-layered elastic half-space. The general expressions of internal deformation fields due to a moment tensor in an elastic-viscoelastic layered half-space can be obtained applying the correspondence principle in linear viscoelasticity to the elastic solution. In this presentation, as examples of numerical computation, we show the internal velocity fields caused by steady plate divergence at mid-ocean ridge. We also show the change in internal stress fields associated with magmatic intrusion.